Problem: Jessica is 28 years younger than Daniel. Daniel and Jessica first met 3 years ago. Ten years ago, Daniel was 5 times older than Jessica. How old is Daniel now?
Explanation: We can use the given information to write down two equations that describe the ages of Daniel and Jessica. Let Daniel's current age be $d$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $d = j + 28$ Ten years ago, Daniel was $d - 10$ years old, and Jessica was $j - 10$ years old. The information in the second sentence can be expressed in the following equation: $d - 10 = 5(j - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to solve our first equation for $j$ and substitute it into our second equation. Solving our first equation for $j$ , we get: $j = d - 28$ . Substituting this into our second equation, we get the equation: $d - 10 = 5($ $(d - 28)$ $ -$ $ 10)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $d - 10 = 5d - 190$ Solving for $d$ , we get: $4 d = 180$ $d = 45$.